document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=268505>Question 268505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if roulette were fair, how much should the house pay a player who bets $20 on a single number and it comes up? the odds against winning are 36:1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196759 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if roulette were fair, how much should the house pay a player who bets $20 on a single number and it comes up? the odds against winning are 36:1<BR>\n" );
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document.write( "P(losing) = 36/37<BR>\n" );
document.write( "P(winning) = 1/37<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Let \"x\" be the amount the house pays.<BR>\n" );
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document.write( "Note: Expected pay is zero if the game is \"fair\".<BR>\n" );
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document.write( "E(x) = (winnings)P(win) + (loss)P(lose)<BR>\n" );
document.write( "E(x) = (x-20)(1/37) + (-20)(36/37) = 0<BR>\n" );
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document.write( "Multiply thru by 37 and solve for \"x\":<BR>\n" );
document.write( "x-20 -20(36) = 0<BR>\n" );
document.write( "x = 20*36+20<BR>\n" );
document.write( "x = $740<BR>\n" );
document.write( "===============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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